Among the dozens of definitions, available complexity can be defined as repudiating a perceptibly complex phenomenon. It has its origins in the Latin word ‘complexus’ meaning twisted together or entwined. There are more than two components which form a complex, and the bonding between the two is such that it is not easy to separate them. The Oxford Dictionary explains something as complex if it is made of several closely linked parts. There is a dualism in parts that are both connected yet distinct. Thus, a system would be more complex if the parts are distinguishable and there are more links between them. The more the parts, the more extensive the models are, and they need a lot of time to be computed or searched. The components of a complex cannot be detached without rescinding it, therefore, the technique of analysis or decomposing them into autonomous components cannot be used to develop or simplify such reproductions. This means that it is hard to make complex objects, it is also difficult to use such objects for control or prediction and the issues will be problematic to solve. This is mainly the meaning which is usually used in describing complex.

The facets of dissimilarity and connection define two dimensions characterizing complexity. Dissimilarity parallels diversity to heterogeneity to the point that various fragments of complex perform inversely. Connection counters restraint to severance to the point that every dart is not independent but that the knowledge of one component sets up the base for features of other components. Dissimilarity is leads in the edge to bedlam for instance in gas, where a specific gas molecule has an independent position than the other molecules present in it.

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Connection on the other hand leads to order for instance in a crystal where the position of a molecule depends on the position of the other molecules that are connected to it.

Presence of both dissimilarity and connection are imperative for complexity to exist.

The easiest way to craft order is through the theory of symmetry which is agreement in arrangement, dimensions and due proportion or a sense of proportion and balance. Just a part of the pattern is enough to remodel a symmetric pattern.

The bigger the group of symmetry transformations is the lesser work or fragment is required for remodelling the entire pattern.

Take the example of a crystal – its structure is invariant under a distinct group of rotations and translations. Just a small group of linked molecules is enough to determine the position of the other molecules (various transformations are applied).

Empty space is usually in order or symmetric and its properties doesn’t change despite the transformation of any part. Any small part can be used to create a different part.

The highest disorder also is categorised by symmetry which is of probabilities that a constituent may be found at a specific position. This symmetry is not of the actual positions of the constituents. Say for instance, gas is homogeneous all positions contains a gas molecule. These individual molecules are unevenly spread but considering on an average, the centre of gravity of huge assemblies of molecules it will be symmetric based on the law of large numbers. Similarly the Brownian motion (the movement of microscopic particles randomly in the fluid because of the continued molecular bombardment of the surrounding medium) can be explained by the point that all probable transitions are correspondingly possible.

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When there is no symmetry, there is complexity because no component of a complex object offers proper information to statistically predict the properties of the other components.This shows how difficult it is to model things with complex systems.

When complexity is spoken of in scale of dimension, then the human body is the best example. If zoomed in then there are several complex structures that are revealed such as cells, organism, nucleons, atoms, polymers, elementary particles, monomers, organs, and tissues. There are similarities which are apparent between the levels such as organs and organelles. The connection and dependence between the various levels are different and depends on the connection, distinction and symmetry break-up.

In short, the level of complexity intensifies when connection and distinction of aspects or components increase in several dimensions.

The procedure of proliferation of variety can be termed as differentiation, and the procedure of proliferation in the strength of connections can be termed as integration.

There will always be an idiosyncratic element entailed in the choice of an observer of which facets of a system can be modelled. The dependability of models will be based on how independent are the features that were included in the model and those that were not a part of it. The level of independence will be marked by the unbiased complexity of the system.

Thus, complexity symbolizes the performance of a model or system whose parts interact in different ways. There is no rational greater instruction to explain the different probable interactions. These interactions culminate in a higher order of emergence meaning the whole is greater than the parts, or in other words, the whole has certain properties that the parts don’t have individually. These properties exist as a result of the interaction between these parts of the model. Complex Systems Theory is based on the study of complex connections at different levels.

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Depending on the type of system the definition of complexity can usually differ because the components or parts included in it may give different interactions with the elements that are in that system but may interact differently with other elements outside the system. Several definitions presume that complexity states a condition of several components or elements and several forms of relationships between the components. But what one may see as complex and/or simple is relative and alters with time.

American scientist, science administrator, and mathematician Warren Weaver hypothesized two forms of complexity in 1948:
Organized Complexity
Disorganized Complexity

The occurrences of organized complexity deal concurrently with a sizable number of aspects that are connected with one system. Disorganized complexity, on the other hand, is understood through statistical procedures and theory of possibility.

Weaver’s thoughts in the paper on Complexity released in 1948 reveal that the methods that exemplify perceptions of multiple elements, state spaces, systems, and multiple relational regimes can be briefed that complexity ascends from the various discernible relational regimes in a definite system.

Would you like to read more about this topic? This book might interest you: Complexity.